Browsing by Author "Webb, John"
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- ItemOpen AccessErrors in South African secondary school mathematics textbooks(1998) Harris, Carol; Webb, JohnSince 1960 various new topics were introduced into the South African mathematics syllabus for high schools. This was generally described as "New Maths". These topics were characterised by an emphasis on mathematical structure (set theory, groups, rings and fields, the construction of the real number system, relations and functions, vectors and mathematical induction). Textbooks that were published in South Africa during this time have been found to contain numerous significant mathematical errors, especially in connection with these new topics. This project has entailed the collection, classification and commentary on these problems. It has involved a study of a range of texts from Standards 6 to 10. The methodology utilised entailed reading as many maths textbooks as we could find in libraries such as Education libraries. Other sources of textbooks were from the library of the Mathematics Education Project (MEP)(of the University of Cape Town), private collections and second hand bookshops. Some misconceptions arise across a range of texts indicating that either a general misunderstanding has occurred or that authors have used one another's work in their research. We conducted a search for mathematical errors and not minor misprints, arithmetical slips, algebraic errors, mistakes in answers at the back of the book, spelling or grammatical mistakes.
- ItemOpen AccessA learning theory approach to students' misconceptions in calculus(1998) Bowie, Lynn Heather; Ensor, Paula; Webb, JohnThis study analyses students' errors in calculus through the lens of learning theories. The subjects in this study were 117 students enrolled in a calculus course for students from disadvantaged educational backgrounds at the University of Cape Town. A coding scheme to categorise the errors that these students made in the final examination was developed. This categorisation was supported by error data generated through the administration of a conceptual test and follow-up interviews. The pattern of errors in the coding scheme suggests that the students' perception of algebra is largely that of a "game of letters". As a result of this their construction of calculus knowledge is based on the rehearsal of algorithmic procedures. Their errors indicate that they develop linking and extending mechanisms to deal with the multiplicity of rules that are generated from this process of rehearsal.
- ItemOpen AccessNorm-determining subspaces(1970) Sarembock, Sandra Jacqueline; Webb, JohnThis thesis will centre on the concept of norming subspaces in the dual of a Banach space. We shall consider a weakly-dense subspace V of E', and the natural norm it generates on E. If this new norm is equivalent to the original norm on E, then V is called norming or norm-determining.
- ItemOpen AccessPromoting understanding in mathematical problem-solving through writing : a Piagetian analysis(2007) Craig, Tracy S; Dunne, Tim; Webb, JohnIncludes bibliographical references (leaves 204-221).